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### Solutions for Act III Scene 4 - Flowcharts

The specificity of some of the questions in these flowcharts suggests they are written for particular groups of things, and keeping this in mind, we can use the peculiarities of some of the questions as well as the number of squares per chart to extrapolate what each group might be. Some of the questions were deliberately written vaguely in an attempt to somewhat obscure the theme for each chart.

For instance, the first chart suggests the objects are animals/people that are also related to properties involving numbers, colours (including silver), and edges that may be straight or rough. This all points to the animals/people being on coins, and indeed the set of the six Australian coins seems fit the bill. Filtering all six coins through the chart seems to work out, with each coin's symbol ending up in a different square, and all arrows being used.

Working out each other chart's set and order gives the following in order (note the lists are based on how they were at the beginning of the hunt - in particular, Rapunzel was only officially added to the list of Disney princesses on the last day of the hunt):

 Group Resulting order current Aus coin images kangaroo, platypus, Aboriginal elder, echidna, lyrebird, coat of arms colours of the rainbow violet, orange, green, indigo, red, blue, yellow chess pieces castle, pawn, queen, knight, bishop, king solar system's planets Earth, Mercury, Uranus, Neptune, Venus, Mars, Jupiter, Saturn Disney princesses Snow White, Pocahontas, Mulan, Jasmine, Ariel, Aurora, Belle, Cinderella, Tiana initial X-Men members Cycops, Iceman, Beast, Marvel Girl, Angel Pixar films Up, Cars, Toy Story 3, Monsters Inc., WALL-E, Toy Story, Cars 2, A Bug's Life, Finding Nemo, Ratatouille, The Incredibles, Toy Story 2

Now that we have a bunch of orderings, we need to work out what to do with them. What needs to be noticed is that the path each element of each set takes is also important, which is hinted at by the fact some questions are unnecessarily phrased negatively. Indeed, for each word filtered through a flowchart, we have a unique string of yes and no answers associated with it - e.g. in the first chart, KANGAROO (from the \$1 coin) follows the path YES-NO-NO.

A logical conversion of each string is to read each YES as a 1 and each NO as a 0, which will then give a binary number associated with each word (so KANGAROO's path becomes 100, or 4 in binary). The first chart gives in order the pairs: KANGAROO/4, PLATYPUS/2, ABORIGINAL ELDER/7, ECHIDNA/5, LYREBIRD/4, COAT OF ARMS/8. Indexing into each word by the number associated with each word gives GLIDER, another word. Indeed doing this for each chart gives the words:

 current Aus coin images: GLIDER colours of the rainbow: TANGELO chess pieces: CANNON solar system's planets: HESPERIA Disney princesses: ESMERALDA initial X-Men members: CABLE Pixar films: PARTLY CLOUDY

While these words might seem at first unrelated, the trick here is to notice that each new word is almost a member of its associated chart's group: The glider is on the no-longer-used Australian one-cent coin, tangelo is a colour not recognised as one of the rainbow seven, the cannon is a piece in Chinese chess, Hesperia is a minor planet in the solar system, Esmeralda is a Disney character sometimes used in the Disney princess marketing, Cable is a later member of the X-Men, and Partly Cloudy is a Pixar short film.

Given this link between words and charts, the next thing to do is filter the new words through their charts once more. This time we do not care which square each word ends up in, but only which path it takes (which is not necessarily any of the paths taken by the original elements of the group). This gives: GLIDER/5, TANGELO/6, CANNON/1, HESPERIA/6, ESMERALDA/1, CABLE/1, PARTLY CLOUDY/6.

Indexing in again, the letters we end up with are ELCRECY. This anagrams to give the word RECYCLE, which somewhat describes what we've done throughout the puzzle (we've perused each flowchart several times to determine the results of each element in the group, have then recycled each flowchart by filtering through the newly-found words, and recycled the order of the final set of letters to arrive at the answer).

Note: While the puzzle originally had the flowcharts presented in order so that no anagramming was required after extracting the seven letters, it was decided to mix the order up in the end because it circumvented people solving the puzzle with only a handful of groups discovered, and made the PDF one page less long.